# How to Solve Supply & Demand Equations

The laws of supply and demand were probably among the first things taught in Economics 101. You may have learned them selling candy and gift wrap for your kid’s school or sports team. Simply put, the laws of supply and demand reflect the relationship of how much of something a producer or manufacturer wants to sell at a price, what the price should be and how many consumers are willing to buy at that price. The price that is set is called the equilibrium. This is where the producer who makes the product, and the consumer, who buys the product to satisfy a need or want, find that sweet spot.

When the producer and the consumer arrive at that magic number, it’s the result of an equation that is not as complex as it seems on the surface. We take the Quantity Demand figure, which we will call Qd. Then we take the Quantity Supply figure, which we will call Qs. To get to that sweet spot, keep in mind that quantity demanded must equal quantity supplied. This calculation assumes there are no outside influences that may affect the price. In other words, the item hasn’t become a fad, or, there isn’t some form of external baggage that would cause consumers to reject it.

Now is the time to figure out the quantity you will need, based on supply and demand. Plot the demand and supply numbers that you are using onto the demand and supply curves. Think of price as the vertical and quantity as the horizontal. So here’s an example:

D(demand) = 20 - 2P(price). So you are taking that demand figure of 20, and subtracting from it two multiplied by the price. S(supply) = -10 + 2P(price). So supply equals minus 10 multiplied by two multiplied by the price.

Here’s where the equation works:

D = 20 - 2P and S = -10 + 2P will become 20 - 2P = -10 + 2P. That simplifies to 20 + 10 = 4P, or 30 divided by 4, which equals price. Price is then 7.5, or $7.50 if we're working in single dollars. To find quantity, put 7.5 into one of the equations. Q = 20 - (2 x 7.5). Your quantity equals five, which is the sweet spot where quantity demanded equals quantity supplied (Qd equals Qs).

When trying to figure out demand, remember that a demand curve usually arcs downward, because most people would rather pay less and get more of the product. Any changes in factors that don’t involve price would cause a shift in the demand curve. Changes in the price can be traced along a fixed demand curve.

Next, you want to figure out your supply curve. The ideal number of products in the market depends not only on the price but similar products put out by your competitors, technology, labor and production costs. You want to consider various prices, and the quantity offered at each price while keeping other factors constant. Now you’ve got your supply curve.

Equilibrium price is where demand and supply meet. If buyers want more of what you are selling at the current price, you can probably raise your price. If they’re not buying most of what you’re producing, then your suppliers will want you to lower the price.